The Verge did a decent article talking about the exact thing you've quoted. I wouldn't be able to do a better job of explaining it in my own words, so here is a quote from the article, with emphasis added by me:
If you assume this applies to Windows 10 then it sounds like Microsoft is going to constantly scan your PC to make sure you don't have any illegal copies of Call of Duty. The reality is probably very different as this applies primarily to the services powering Windows 10. This agreement applies to Xbox and Xbox Live, so it's safe to assume Microsoft will continue issuing Xbox software updates that block certain peripherals and pirated games. The software maker has been doing this for years on the Xbox side, and it's unlikely the company would transfer such a complex disc-based detection system over to the PC.
I could imagine "unauthorized hardware" - when you consider this applies to the Xbox - is things like knock-off controllers, dodgy HDDs... chips that circumvent DRM (or anything that circumvents DRM.)